breed [points point]  

breed [points2 point2]

​

to setup

​

  clear-all

  resize-world -100 100 -100 100

  set-patch-size 2

  ask patches [ set pcolor [235 235 235]]

  setup-axespoints

  setup-xaxis

  setup-yaxis

end

​

to-report slide-maximum 

  report 1

end

​

to-report slide-minimum 

  report -1

end

​

to-report slide-inc 

  report .1

end

​

to setup-axespoints

  let x-axes patches with [

    pycor = 0

    and 

    abs pxcor = max-pxcor

  ]

  let y-axes patches with [

    pxcor = 0

    and 

    abs pycor = max-pycor

  ]

  ask patches with [

    pxcor = 0

    and pycor = 0

  ] [

    sprout-points 1 [

      setup-appearance

    ]

  ]  

  ask x-axes [

    sprout-points 1 [

      setup-appearance

    ]    

  ]

  ask y-axes [

    sprout-points 1 [

      setup-appearance

    ]    

  ]

end

​

to setup-xaxis

  let beginpt one-of turtles with [ xcor = min-pxcor and ycor = 0 ]

  let endpt one-of turtles with [ xcor = max-pxcor and ycor = 0 ]

  let origin one-of turtles with [ xcor = 0 and ycor = 0 ]

  ask beginpt [ create-link-with origin ]

  ask origin [ create-link-with endpt ]

end

​

to setup-yaxis 

  let beginpt one-of turtles with [ ycor = min-pycor and xcor = 0 ]

  let endpt one-of turtles with [ ycor = max-pycor and xcor = 0 ]

  let origin one-of turtles with [ xcor = 0 and ycor = 0 ]

  ask beginpt [ create-link-with origin ]

  ask origin [ create-link-with endpt ]

end

​

to setup-appearance 

  if breed = points [

    show-turtle

    set color black

    set shape "circle"

    set size .3

  ]

  if breed = points2 [

    show-turtle

    set color red

    set shape "circle"

    set size .3

  ]

  ask turtles with [xcor = 0 and ycor = 0] [

    ask my-links [

      set color gray

    ]

  ]

end

​

​

to plotpoints

  let xcord min-pycor

  loop [

    if xcord = max-pxcor [ stop ]

    let y calculate-function xcord

    ;;if round y < max-pycor [ show round y] 

    ask patches with [ pxcor = xcord and pycor = round y] [sprout-points 1 [ setup-appearance ]]

    set xcord xcord + 1

  ]

end

​

to connect 

  let xcord min-pxcor

  loop [

    if xcord = max-pxcor - 1[ stop ]

    let y calculate-function xcord

    if y < max-pycor and y > min-pycor [

      let prev one-of turtles with [ xcor = xcord and ycor = round y]

      ;ask prev [set label-color red set label ","]

      let nexty calculate-function (xcord + 1)

      if nexty < max-pycor and y > min-pycor [

        let next one-of turtles with [ xcor = (xcord + 1) and ycor = round nexty]

        ;ask next [set label-color blue set label "'"]

        if y > min-pycor and y < max-pxcor and nexty > min-pycor and nexty < max-pycor [

          ask prev [create-link-with next ask my-links [set color black]]

        ]

      ]

    ]

​

    set xcord xcord + 1

  ]

end

​

to graph

  plotpoints

  connect

  plottaylor

  connecttaylor

  ;ask turtles with [xcor = 0 and ycor = 0] [

    ;ask my-links [

      ;set color black

    ;]

  ;]

end 

​

to-report calculate-function [input]

  let value constant + x1-coefficient * (input) / max-pxcor + x2-coefficient * ((input) / max-pxcor)^(2) + x3-coefficient * ((input) / max-pxcor)^(3) + x4-coefficient * ((input) / max-pxcor)^(4) + x5-coefficient * ((input) / max-pxcor)^(5) + x6-coefficient * ((input) / max-pxcor)^(6) + x7-coefficient * ((input) / max-pxcor)^(7)

  let newvalue precision (value * max-pxcor )  5

  report newvalue

end

​

to-report taylor-approximation [input] 

  let value constant + x1-coefficient * ((input) / max-pxcor) + x2-coefficient * ((input) / max-pxcor)^ 2 / factorial 2 + x3-coefficient * ((input) / max-pxcor)^ 3 / factorial 3 + x4-coefficient * ((input) / max-pxcor)^ 4 / factorial 4 + x5-coefficient * ((input) / max-pxcor)^ 5 / factorial 5 + x6-coefficient * ((input) / max-pxcor)^ 6 / factorial 6 + x7-coefficient * ((input) / max-pxcor)^ 7 / factorial 7 

  let newvalue precision (value * max-pxcor )  5

  report newvalue

end

​

to plottaylor

  let xcord min-pycor

  loop [

    if xcord = max-pxcor [ stop ]

    let y taylor-approximation xcord

    ;;if round y < max-pycor [ show round y] 

    ask patches with [ pxcor = xcord and pycor = round y] [sprout-points2 1 [ setup-appearance ]]

    set xcord xcord + 1

  ]

end

​

to connecttaylor

  let xcord min-pxcor

  loop [

    if xcord = max-pxcor - 1[ stop ]

    let y taylor-approximation xcord

    if y < max-pycor and y > min-pycor [

      let prev one-of turtles with [ xcor = xcord and ycor = round y]

      ;ask prev [set label-color red set label ","]

      let nexty taylor-approximation (xcord + 1)

      if nexty < max-pycor and y > min-pycor [

        let next one-of turtles with [ xcor = (xcord + 1) and ycor = round nexty]

        ;ask next [set label-color blue set label "'"]

        if y > min-pycor and y < max-pxcor and nexty > min-pycor and nexty < max-pycor [

          ask prev [create-link-with next ask my-links [set color red]]

        ]

      ]

    ]

​

    set xcord xcord + 1

  ]

end

​

to-report factorial [input]

  if input = 1 [ report 1 ]

  report input * factorial (input - 1)

end